Maps between some different kinds of contraction function: The finite case

In some recent papers, the authors and Peter Gärdenfors have defined and studied two different kinds of formal operation, conceived as possible representations of the intuitive process of contracting a theory to eliminate a proposition. These are partial meet contraction (including as limiting cases full meet contraction and maxichoice contraction) and safe contraction. It is known, via the representation theorem for the former, that every safe contraction operation over a theory is a partial meet contraction over that theory. The purpose of the present paper is to study the relationship more finely, by seeking an explicit map between the component orderings involved in each of the two kinds of contraction. It is shown that at least in the finite case a suitable map exists, with the consequence that the relational, transitively relational, and antisymmetrically relational partial meet contraction functions form identifiable subclasses of the safe contraction functions, over any theory finite modulo logical equivalence. In the process of constructing the map, as the composition of four simple transformations, mediating notions of bottom and top contraction are introduced. The study of the infinite case remains open.     

Bilinguals in a monolingual and a bilingual speech mode: The effect on lexical access

The time course of lexical access in fluent Portuguese-English bilinguals and in English speaking monolinguals was examined during the on-line processing of spoken sentences using the phoneme-triggered lexical decision task (Blank, 1980). The bilinguals were tested in two distinct speech modes: a monolingual, English or Portuguese, speech mode, and a bilingual, code-switching, speech mode. Although the bilingual’s lexical decision response times to word targets in the monolingual speech modes were identical to those of the monolingual subjects, their response times to code-switched word targets in the bilingual mode were significantly slower. In addition, the bilinguals took longer to detect nonwords in both the monolingual and bilingual modes. These results confirm that bilinguals cannot totally deactivate their other language when in a monolingual speech mode. It is hypothesized that bilinguals search both lexicons when confronted with nonwords, even when in a totally monolingual mode, and that they search the base-language lexicon before the other lexicon when in a bilingual, code-switching, speech mode.